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Large friction-high force fields limit for the nonlinear Vlasov–Poisson–Fokker–Planck system
Glassey-Strauss representation of Vlasov-Maxwell systems in a Half Space
1. | Department of Mathematics, Rutgers University, Piscataway, NJ 08854, USA |
2. | Department of Mathematics, University of Wisconsin-Madison, Madison, WI 53717, USA |
3. | Department of Mathematical Sciences, Seoul National University, Seoul 08826, Republic of Korea |
Following closely the classical works [
References:
[1] |
Y. Cao and C. Kim, On some recent progress in the Vlasov-Poisson-Boltzmann system with diffuse reflection boundary, Recent Advances in Kinetic Equations and Applications, Springer INdAM Series, 48 (2021). |
[2] |
Y. Cao, C. Kim and D. Lee,
Global strong solutions of the Vlasov-Poisson-Boltzmann system in bounded domains, Arch. Rational Mech. Anal., 233 (2019), 1027-1130.
doi: 10.1007/s00205-019-01374-9. |
[3] |
J. Cooper and W. Strauss,
The initial boundary problem for the Maxwell equations in the presence of a moving body, SIAM J. Math. Anal., 16 (1985), 1165-1179.
doi: 10.1137/0516086. |
[4] |
G. Federici, et al, Plasma-material interactions in current tokamaks and their implications for next step fusion reactors, Nucl. Fusion, 41 (2001). |
[5] |
R. T. Glassey, The Cauchy Problem in Kinetic Theory, Society for Industrial and Applied Mathematics, 1996.
doi: 10.1137/1.9781611971477. |
[6] |
R. T. Glassey and J. Schaeffer,
The relativistic Vlasov-Maxwell system in two space dimensions. Ⅰ, Arch. Rational Mech. Anal., 141 (1998), 331-354.
doi: 10.1007/s002050050079. |
[7] |
R. T. Glassey and J. Schaeffer,
The relativistic Vlasov-Maxwell system in two space dimensions. Ⅱ, Arch. Rational Mech. Anal., 141 (1998), 355-374.
doi: 10.1007/s002050050080. |
[8] |
R. T. Glassey and W. A. Strauss,
Singularity formation in a collisionless plasma could occur only at high velocities, Arch. Rational Mech. Anal., 92 (1986), 59-90.
doi: 10.1007/BF00250732. |
[9] |
R. T. Glassey and W. A. Strauss,
High velocity particles in a collisionless plasma, Math. Methods Appl. Sci., 9 (1987), 46-52.
doi: 10.1002/mma.1670090105. |
[10] |
D. Griffith, Introduction to Electrodynamics, Cambridge University Press, 4th edition, 2017.
![]() |
[11] |
Y. Guo,
Global weak solutions of the Vlasov-Maxwell system with boundary conditions, Comm. Math. Phys., 154 (1993), 245-263.
doi: 10.1007/BF02096997. |
[12] |
Y. Guo,
Regularity for the Vlasov equations in a half space, Indiana Univ. Math. J., 43 (1994), 255-320.
doi: 10.1512/iumj.1994.43.43013. |
[13] |
J. D. Jackson, Classical Electrodynamics, Wiley, 3rd edition, 1998.
doi: 10.1119/1.19136. |
[14] |
X. Liu, F. Yang, M. Li and S. Xu, Generalized boundary conditions in surface electromagnetics: Fundamental theorems and surface characterizations, Appl. Sci., 9 (2019).
doi: 10.3390/app9091891. |
[15] |
J. Luk and R. M. Strain,
A new continuation criterion for the relativistic Vlasov-Maxwell system, Comm. Math. Phys., 331 (2014), 1005-1027.
doi: 10.1007/s00220-014-2108-8. |
[16] |
K. McDonald, Electromagnetic fields inside a perfect conductor, Unpublished note. |
[17] |
T. T. Nguyen, T. V. Nguyen and W. A. Strauss,
Global magnetic confinement for the 1.5D Vlasov-Maxwell system, Kinetic and Related Models, 8 (2015), 153-168.
doi: 10.3934/krm.2015.8.153. |
show all references
References:
[1] |
Y. Cao and C. Kim, On some recent progress in the Vlasov-Poisson-Boltzmann system with diffuse reflection boundary, Recent Advances in Kinetic Equations and Applications, Springer INdAM Series, 48 (2021). |
[2] |
Y. Cao, C. Kim and D. Lee,
Global strong solutions of the Vlasov-Poisson-Boltzmann system in bounded domains, Arch. Rational Mech. Anal., 233 (2019), 1027-1130.
doi: 10.1007/s00205-019-01374-9. |
[3] |
J. Cooper and W. Strauss,
The initial boundary problem for the Maxwell equations in the presence of a moving body, SIAM J. Math. Anal., 16 (1985), 1165-1179.
doi: 10.1137/0516086. |
[4] |
G. Federici, et al, Plasma-material interactions in current tokamaks and their implications for next step fusion reactors, Nucl. Fusion, 41 (2001). |
[5] |
R. T. Glassey, The Cauchy Problem in Kinetic Theory, Society for Industrial and Applied Mathematics, 1996.
doi: 10.1137/1.9781611971477. |
[6] |
R. T. Glassey and J. Schaeffer,
The relativistic Vlasov-Maxwell system in two space dimensions. Ⅰ, Arch. Rational Mech. Anal., 141 (1998), 331-354.
doi: 10.1007/s002050050079. |
[7] |
R. T. Glassey and J. Schaeffer,
The relativistic Vlasov-Maxwell system in two space dimensions. Ⅱ, Arch. Rational Mech. Anal., 141 (1998), 355-374.
doi: 10.1007/s002050050080. |
[8] |
R. T. Glassey and W. A. Strauss,
Singularity formation in a collisionless plasma could occur only at high velocities, Arch. Rational Mech. Anal., 92 (1986), 59-90.
doi: 10.1007/BF00250732. |
[9] |
R. T. Glassey and W. A. Strauss,
High velocity particles in a collisionless plasma, Math. Methods Appl. Sci., 9 (1987), 46-52.
doi: 10.1002/mma.1670090105. |
[10] |
D. Griffith, Introduction to Electrodynamics, Cambridge University Press, 4th edition, 2017.
![]() |
[11] |
Y. Guo,
Global weak solutions of the Vlasov-Maxwell system with boundary conditions, Comm. Math. Phys., 154 (1993), 245-263.
doi: 10.1007/BF02096997. |
[12] |
Y. Guo,
Regularity for the Vlasov equations in a half space, Indiana Univ. Math. J., 43 (1994), 255-320.
doi: 10.1512/iumj.1994.43.43013. |
[13] |
J. D. Jackson, Classical Electrodynamics, Wiley, 3rd edition, 1998.
doi: 10.1119/1.19136. |
[14] |
X. Liu, F. Yang, M. Li and S. Xu, Generalized boundary conditions in surface electromagnetics: Fundamental theorems and surface characterizations, Appl. Sci., 9 (2019).
doi: 10.3390/app9091891. |
[15] |
J. Luk and R. M. Strain,
A new continuation criterion for the relativistic Vlasov-Maxwell system, Comm. Math. Phys., 331 (2014), 1005-1027.
doi: 10.1007/s00220-014-2108-8. |
[16] |
K. McDonald, Electromagnetic fields inside a perfect conductor, Unpublished note. |
[17] |
T. T. Nguyen, T. V. Nguyen and W. A. Strauss,
Global magnetic confinement for the 1.5D Vlasov-Maxwell system, Kinetic and Related Models, 8 (2015), 153-168.
doi: 10.3934/krm.2015.8.153. |
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